Once the existence of ergodic SRB measures has been established, a natural question to ask is when the SRB measure is unique. In [1]}, it is shown that in the case of a \(C^{1+\alpha }\)  diffeomorphism \(f\)  of a compact surface, if \(f\)  is topologically transitive, then \(f\)  admits at most one SRB measure. A similar result may be proven for singular hyperbolic attractors, provided a certain regularity condition on the stable foliation (Theorem REF , also [2]}). The regularity condition needed is local continuity, which roughly means that the smooth functions \(E^s(x) \rightarrow M\)  defining the local stable leaf \(W_{\mathrm {loc}}^s(x)\)  vary continuously with \(x \in K \setminus N\) , where \(E^s(x) \subset T_x M\)  is the stable subspace at \(x\) . In this paper, we show that a singular hyperbolic map for which the stable foliation is locally continuous admits a unique SRB measure if and only if the map is topologically transitive.
